A new culture starts, Spengler held, when persons in a dying, static, or purposeless society—at first only a few visionaries, often widely isolated—begin to see their surroundings from a new perspective. This intruding viewpoint, he suggests, becomes a driving force that grows to dominate their thinking like a Jungian archetype. Step by step the increasing influence of this new point of view transforms that entire society—its political and social structures, its business organizations and commercial practices, its technologies, mathematics, religious beliefs, music and visual arts, and architecture—to exemplify this unique outlook; he terms it the culture’s “prime symbol.”
The process, always similar, takes 1000–1200 years to run its course. In their final 200–300 years, Spengler said, all civilizations stiffen into rigidity and formalism; creativity dies out and cynicism surges...
Spengler made detailed analyses of six cultures, illustrating in charts of parallel columns how five passed through the same changes at corresponding stages in their development. Spengler described the dominating viewpoints of these cultures as:
- Egyptian—An arrow-straight path into eternity.
- Chinese—An indirect, seemingly-meandering path towards life’s goal.
- Hindu—Prime symbol not diagnosed by Spengler. Possibly nirvana, extinction through fulfillment. (The mathematical concept of zero was invented by the Hindu culture, which passed it to the West via Arabic mathematicians).
- Classical (Greek-Roman)—The tangible, free-standing object, exemplified by the nude statue.
- Magian (early Christianity, Mohammedanism)—A magical closed cavern, from whose upper reaches divine grace descends like a golden mist.
- Western (present culture, born in Western Europe about 1000 A.D.)—A spiritual reaching out into boundless space.
The ossified forms of exhausted cultures, he wrote, can persist like pyramids for thousands of years. A new culture may emerge from their detritus or from within a society hitherto lacking a prime symbol. If the new culture’s start overlaps a dominant but dying culture, its early development will be masked and for a time, warped by that prior culture.
Cedric Villani
My main research interests are in kinetic theory (especially Boltzmann equation and its variants; see my long review paper), and optimal transport and its applications (I wrote a book on that subject too; and then another book). More generally, I am fond of subjects which combine several (if not all) of the following themes: evolution partial differential equations, fluid mechanics, statistical mechanics, probability theory, smooth and nonsmooth "metric" Riemannian geometry, and functional inequalities with geometric content.
http://en.wikipedia.org/wiki/C%C3%A9dric_Villani
